Originally posted by CM123
Good point about the friction.
Looks good at a brief glance, I haven't had much time to go over it - two questions however...
How did you calculate the moment of inertia, and can gravity have a component perpendicular to the plank when it is not at rest?
Also, I think SHM can have large oscillations, just not in this case.
I looked up the moment of inertia of a rod (ML^2/12) about the centre, then used the parallel axis theorem to calculate it about the pivot point (I' = I + Mx^2).
I don't think there are any problems with using the component of gravity. There is an approximation because I've neglected the fact that the pivot point is moving, but that comes out as O(a^3) I think.
Yes, SHM can have large oscillations - in that case the equation of motion would have been exact, and I wouldn't have had to approximate.